Rapid Quantification of Pharmaceuticals via 1H Solid-State NMR Spectroscopy

The physicochemical properties of active pharmaceutical ingredients (APIs) can depend on their solid-state forms. Therefore, characterization of API forms is crucial for upholding the performance of pharmaceutical products. Solid-state nuclear magnetic resonance (SSNMR) spectroscopy is a powerful technique for API quantification due to its selectivity. However, quantitative SSNMR experiments can be time consuming, sometimes requiring days to perform. Sensitivity can be considerably improved using 1H SSNMR spectroscopy. Nonetheless, quantification via 1H can be a challenging task due to low spectral resolution. Here, we offer a novel 1H SSNMR method for rapid API quantification, termed CRAMPS–MAR. The technique is based on combined rotation and multiple-pulse spectroscopy (CRAMPS) and mixture analysis using references (MAR). CRAMPS–MAR can provide high 1H spectral resolution with standard equipment, and data analysis can be accomplished with ease, even for structurally complex APIs. Using several API species as model systems, we show that CRAMPS–MAR can provide a lower quantitation limit than standard approaches such as fast MAS with peak integration. Furthermore, CRAMPS–MAR was found to be robust for cases that are inapproachable by conventional ultra-fast (i.e., 100 kHz) MAS methods even when state-of-the-art SSNMR equipment was employed. Our results demonstrate CRAMPS–MAR as an alternative quantification technique that can generate new opportunities for analytical research.


Table of Contents
Discussion S1. Mixture sample preparation procedure S5 Discussion S2. Additional SSNMR experimental and data processing details S6 Discussion S3. Phasing 1 H CRAMPS spectra for MAR S10 Discussion S4. Scaling and aligning the 1 H CRAMPS spectra for MAR S16 Discussion S5. Influence of spectral binning on CRAMPS-MAR S22 Figure S1. Chemical structures of Pio, PioHCl, and Org OD 14 S4 Figure S2. Schematic outlining the CRAMPS-MAR Procedure S9 Figure S3. In-phase and ± 1.5°(0 th order) out-of-phase Pio spectra S12 Figure S4. Influence of 0 th order phasing on CRAMPS-MAR fits S13 Figure S5. Influence of 1 st order phasing on CRAMPS-MAR fits S14 Figure S6. In-phase and ± 60°(1 st order) out-of-phase Pio spectra S15 Figure S7. 1 Table S1. Amounts of Pio and PioHCl in the Pio/PioHCl binary mixtures S5 Table S2. Amounts of Org-I and Org-II in the Org-I/-II binary mixtures S5 Table S3. 1 H wDUMBO acquisition parameters S7 Table S4. 1 H  13 C CP/MAS inversion recovery acquisition parameters S8 S3   Table S5. 1 H one-pulse acquisition parameters S8 Table S6. CRAMPS-MAR fit results using scale-by-reference and scale-by-difference S21 Table S7. Binning conditions used to construct the spectra in Figure S9. S26 Table S8. Pio/PioHCl sample compositions and the corresponding CRAMPS-MAR results S29 S4 Figure S1. The chemical structures of (a) Pio, (b) PioHCl, and (c) Org OD 14.

Mixture Sample Preparation Procedure
To prepare the bicomponent mixtures, the respective components (i.e., Pio and PioHCl, Org-I and Org-II) were weighted, then mixed for 12 to 48 hrs using a vortex mixer. The samples were manually inverted a few times during mixing to ensure homogeneity. The sample weights used to prepare the mixtures are given in Table S1 and S2.

Additional SSNMR Experimental and Data Processing Details
For the 1 H wDUMBO experiments, the sample spinning speed (11.1 kHz) was optimized based on the 1 H spectral resolution of glycine. 1 To minimize phase transient effects, and thus maximize spectral resolution, the probe tuning frequency was also optimized. 2 This was accomplished by carefully detuning the probe until the highest resolution 1 H wDUMBO spectrum was obtained for glycine. The transmitter offset frequency was adjusted to avoid overlap between rotary resonance frequency (RRF) lines and the sample signals while preserving spectral resolution. 3 The 1 H wDUMBO acquisition parameters are given in Table S3. The 1 H longitudinal relaxation time (T1) was measured using linear-ramped cross-polarization (CP)/MAS inversion recovery with 13 C detection. The corresponding acquisition parameters are provided in Table S4.
For the ultrafast MAS 1 H SSNMR spectra, the experiments were performed with a onepulse experiment. The corresponding acquisition parameters are provided in Table S5.
For MAR, binning was accomplished via equidistant binning, which gives uniform bin widths. Fitting was only conducted on spectral regions with sample signals, and the regions were represented by the same number of data points for a given bicomponent system (i.e., Pio/PioHCl or Org-I/-II).

Phasing 1 H CRAMPS spectra for MAR
For an accurate CRAMPS-MAR analysis, the pure component spectra must represent the mixture spectrum. Therefore, the spectra must be in-phase with each other. We have investigated the importance of phasing for CRAMPS-MAR using the Pio 90 % dataset. Successful CRAMPS-MAR quantification was achieved when the pure component and mixture spectra are in-phase ( Figure S3a). The composition of Pio was found to be 87.2 to 89.0 wt %, agreeing with the composition determined by sample weight (87.5 to 88.7 wt %).
To examine the influence of 0 th order phasing, the Pio spectrum was adjusted from inphase with the PioHCl and mixture spectra to ± 3° out-of-phase. Figure S4 shows the CRAMPS-MAR results and the corresponding 95% CIs. As expected, the accuracy CRAMPS-MAR decreases as the spectra become more out-of-phase. At large phase deviations (ca. greater than ± 1.5°), the CRAMPS-MAR results become inaccurate. For instance, this is observed when the phase was modified by +3°, where the corresponding CRAMPS-MAR 95 % CI no longer encapsulates the Pio wt % from sample weight. The 95 % CI also increases as the spectra become more out-of-phase, indicating a decrease in precision. Nevertheless, CRAMPS-MAR is robust towards slight differences in 0 th order phasing. This is demonstrated when the phase was varied by ± 1.5°. Figure   S3 shows that the Pio spectra are visibly out-of-phase from the mixture spectrum. However, CRAMPS-MAR still provided an accurate quantification result. For example, when the phase is varied by -1.5°, the composition of Pio was determined to be 86.1 to 87.7 wt %, agreeing with the 87.5 to 88.7 wt % calculated from the sample weight. Moreover, the 95 % CIs were also comparable to those obtained from the in-phase spectra (0.8 to 1.1 wt % vs. 0.9 wt %), indicating S11 that slight changes in phasing does not influence fit precision. Thus, small deviations in 0 th order phasing will not be detrimental to the CRAMPS-MAR results.
To investigate the influence of 1 st order phasing, the Pio spectrum was adjusted from inphase to ± 100° out-of-phase. Figure S5 shows the CRAMPS-MAR fit results and the corresponding 95 % CIs. As compared to 0 th order phasing, CRAMPS-MAR results are less sensitive to 1 st order phasing. When varied by ± 60°, the Pio spectrum is clearly out of phase from the mixture spectrum ( Figure S6). Nonetheless, accurate quantification was still achievable via CRAMPS-MAR. For instance, when the phase was changed by -60°, the Pio composition was found to be 87.3 to 89.2 wt % via CRAMPS-MAR, in agreement with the 87.5 to 88.7 wt % calculated from sample weight. Moreover, the 95 % CIs were also comparable to that of the inphase spectra (ca. 0.9 to 1.1 wt % vs. 0.9 wt %), indicating that the fit precision was not affected.
Even when the phasing was adjusted by ± 100°, CRAMPS-MAR still provided accurate results, albeit a decrease in precision ( Figure S5). Nevertheless, to ensure the best accuracy and precision, the pure component and mixture spectra should still be in-phase to both the 0 th and 1 st order. As CRAMPS-MAR is robust even when the spectra appear to be slightly out-of-phase, visual inspections can be used to evaluate the quality of the phasing. If the spectra appear to be inphase, then the phasing is adequate for a CRAMPS-MAR analysis. S12 Figure S3. The Pio spectrum as (a) in phase and (b and c) out-of-phase with the PioHCl and Pio 90 % spectra. A 0 th order phasing of +1.5 o and -1.5 o were applied to the in-phase Pio spectra to obtain the Pio spectra in (b) and (c), respectively. The pivot point for the phasing is at 0 ppm. No chemical shift scaling or referencing has been applied on the data. S13 Figure S4. To accurately scale and align a spectrum, 2 distinct spectral features are required as σ is applied linearly on the frequency axis (i.e., σν, where ν = a frequency value). 4 Depending on the spectral resolution of m, different methods can be used for scaling and alignment. In the simplest case, m clearly displays at least 2 spectral features for each of the pure components. This is seen in the Pio 70 % mixture spectrum ( Figure S7). Under these circumstances, p1 to pN can be directly scaled and aligned to m using the distinct spectral features.
In more congested spectra, m might not have enough spectral features for one of the components (component 1). Consequently, the spectrum of component 1 (p1) cannot be directly scaled and aligned to m. For example, in the Pio 10 % spectrum, features of pure Pio is no longer clearly observed ( Figure S8a). In these scenarios, we have developed two methods, scale-bydifference and scale-by-reference, to scale and align the pure component spectra of a bicomponent system.

S17
In the scale-by-difference method, the pure component spectrum with at least 2 distinct spectral features (p2) in m is first directly scaled and aligned. The same scaling and alignment factors are then applied on p1 as an initial configuration. A weighted least-squares fit is applied on m, with a weight of 100% assigned to the well-resolved peaks of p2. This fit provides an approximate contribution of p2 to m, allowing a difference spectrum of m -c2p2 to be calculated.
The difference spectrum should resemble p1 and can therefore be used to accurately scale and align p1. A CRAMPS-MAR fit is then performed using the fully scaled and aligned spectra. The procedure for scale-by-difference is demonstrated using Pio 10 % as an example ( Figure S8b).
First, PioHCl is directly scaled and aligned to Pio 10 % as PioHCl signals can be clearly observed at ca. 16 and 1 ppm. The same scaling and alignment factors are then applied on Pio. A weighted least-squares fit is performed with 100 % weight placed on the PioHCl peaks at ca. 16 and 12 ppm. The difference spectrum generated by m-cpioHClppioHCl resembles ppio and was used to rescale and align ppio. A CRAMPS-MAR fit is then performed using ppio and ppioHCl that are properly scaled and aligned.
In the scale-by-reference method, a reference spectrum (mR) is employed. mR must exhibit at least 2 distinct spectral features for each pure component, allowing p1, p2, and m to be directly scaled and aligned to mR. Since all spectra are scaled and aligned to mR, they are also scaled and aligned to each other. The is analogous to secondary chemical shift referencing. Figure   S8c shows scale-by-reference using Pio 10 % as an example. Pio 90 % was used as a reference.
Thus, the PioHCl, Pio, and Pio 10 % spectra can be directly scaled and aligned to Pio 90 %. The resulting Pio and PioHCl spectra are therefore also scaled and aligned to Pio 10 %. S18 Based on the Pio 10 % data set, we found that scale-by-difference and scale-by-reference give comparable fit accuracy and precision (Table S6)

Method
Pio sample weight a 10.6 ± 0.4 scale-by-difference b 10.9 ± 0.7 scale-by-reference b 10.6 ± 0.7 a Errors derived from the uncertainty associated with the analytical balance. b Errors were propagated from the least-squares fitting errors.

Influence of Spectral Binning on CRAMPS-MAR
After applying the appropriate scaling and alignment factors on the spectra, the corresponding data points will occur at different frequencies between different spectra. Thus, the spectra must be binned. Data binning is frequently employed in chemometric analyses of NMR data to eliminate unwanted peak misalignments. [5][6][7] In data binning, the spectrum is divided into small sections (i.e., bins), which is commonly accomplished by using bins of equal widths. 5,6 The spectral area in each bin is then calculated, and the areas are used to represent the spectral intensities. Accordingly, multiple data points are combined into one via binning, and minor peak and/or data point misalignments can be corrected. Nonetheless, binning can drastically reduce the spectral resolution, which can impede accurate data analysis. Here, we investigated the influence of binning on the CRAMPS-MAR results and processing time. For consistency and comparability, the same set of raw 1 H wDUMBO data (PioHCl, Pio, and Pio 10 %) was employed for all our analyses presented in this section. Figure S9 shows the pure PioHCl spectra with various extends of binning. Absolute chemical shift scaling or referencing with respect to glycine was not applied on the spectra, as these procedures are performed after the CRAMPS-MAR fit. The corresponding total number of data points and bin widths are provided in Table S7. Initially, the spectrum consists of 6999 data points, with a separation of 0.5 Hz between each data point. Consequently, the well-resolved signal at ca. 5.4 ppm, which has a full width at half maximum (FWHM) value of ca. 181.2 Hz, is represented by 1199 data points (Table S7). Upon binning, the apparent spectral resolution is maintained if the 5.4 ppm signal is denoted by at least 38 data points. Further binning to less than 38 data points decreases the resolution. In extreme cases, binning "distorts" the spectrum, S23 and the post-binned spectrum no longer represents the pre-binned spectrum. This can be seen in the spectrum where the signal at ca. 5.4 ppm is represented by 5 data points.
If binning decreases the apparent spectral resolution, the CRAMPS-MAR results will be inaccurate and imprecise. Figure S10a shows how binning influences the absolute error. The absolute error is calculated by |Pio wt % predicted by CRAMPS-MAR -Pio wt % calculated from sample weight|. If the 5.4 ppm signal of pure PioHCl is characterized by at least 38 data points, the absolute error remains at 0 wt %. However, if the signal is represented by less than 38 data points, the absolute error increases drastically from 0 to 9 wt %. This is due to a decrease in the apparent spectral resolution, lessening the number of features accessible for the least-squares fit. For example, the PioHCl spectrum displays ca. 12 features when the signal is represented by 1195 data points, but only ca. 5 features at 5 data points ( Figure S9). Thus, drastic binning will decrease the CRAMPS-MAR fit accuracy. Figure S10b shows that binning also influences the CRAMPS-MAR fit precision. As expected, the 95 % confidence interval slowly increases as the number of data points characterizing the 5.4 ppm peak of pure PioHCl decreases from 1195 to 76 However, a drastic increase in the 95 % confidence interval is observed in the region of 38 to 3 data points. This is again due to a decrease in the spectra's apparent resolution, resulting in less spectral features available for a precise fit. When an extreme amount of binning is performed, the 95 % confidence interval is expected to reach 0 since the least-squares equation can be solved analytically. This is seen when the PioHCl peak is represented by 1 data point. We have also investigated the influence of binning on the CRAMPS-MAR analysis time.
The pure component and mixture spectra were binned to give ca. 38 to 1195 data points for the 5.4 ppm peak of pure PioHCl. The post-binned spectra all provide adequate apparent resolution ( Figure S9) and satisfactory fit results ( Figure S10). The data analysis time includes binning, scaling and alignment, sample weight and number of scans normalization, and fitting. As expected, an increase in the number of data points results in an increase in data processing time ( Figure S11).
Nonetheless, the increase was found to be negligible. At 38 data points, the data took 3 seconds to analyze. Increasing the number of data points by a factor of ca. 31 only doubles the analysis time (6 seconds for 1195 data points). Thus, binning has a negligible influence on CRAMPS-MAR data analysis time. However, the number of data points should still be kept at a minimal to avoid any unnecessary increase in time.
S25 Figure S9. (a) The pre-binned 1 H wDUMBO SSNMR spectrum of pure PioHCl and (b-f) the corresponding post-binned spectra. The signal at 5.4 ppm is represented by different number of data points (n.p.) upon binning. No absolute chemical shift scaling or referencing with respect to glycine has been applied on the data. Table S7. The total number of data points and the bin widths used to construct the spectra in Figure S9. The number of data points used to represent the 5.4 ppm signal in each spectrum is also provided.